Articles citing this article

The Citing articles tool gives a list of articles citing the current article.
The citing articles come from EDP Sciences database, as well as other publishers participating in CrossRef Cited-by Linking Program. You can set up your personal account to receive an email alert each time this article is cited by a new article (see the menu on the right-hand side of the abstract page).

Cited article:

Optimal control of the full time-dependent maxwell equations

Vera Bommer and Irwin Yousept
ESAIM: Mathematical Modelling and Numerical Analysis 50 (1) 237 (2016)
https://doi.org/10.1051/m2an/2015041

A guaranteed equilibrated error estimator for the $\mathbf{A}-\varphi$ and $\mathbf{T}-\Omega$ magnetodynamic harmonic formulations of the Maxwell system

Emmanuel Creusé, Serge Nicaise and Roberta Tittarelli
IMA Journal of Numerical Analysis drw026 (2016)
https://doi.org/10.1093/imanum/drw026

On Korn's first inequality for tangential or normal boundary conditions with explicit constants

Sebastian Bauer and Dirk Pauly
Mathematical Methods in the Applied Sciences 39 (18) 5695 (2016)
https://doi.org/10.1002/mma.3954

Discretization of div–curl Systems by Weak Galerkin Finite Element Methods on Polyhedral Partitions

Chunmei Wang and Junping Wang
Journal of Scientific Computing 68 (3) 1144 (2016)
https://doi.org/10.1007/s10915-016-0176-y

On the approximation of electromagnetic fields by edge finite elements. Part 1: Sharp interpolation results for low-regularity fields

Patrick Ciarlet Jr.
Computers & Mathematics with Applications 71 (1) 85 (2016)
https://doi.org/10.1016/j.camwa.2015.10.020

Helmholtz decomposition of vector fields with mixed boundary conditions and an application to a posteriori finite element error analysis of the Maxwell system

Emmanuel Creusé, Serge Nicaise and Zuqi Tang
Mathematical Methods in the Applied Sciences 38 (4) 738 (2015)
https://doi.org/10.1002/mma.3104

A Multiscale Approach and a Hybrid FE-FDTD Algorithm for 3D Time-Dependent Maxwell's Equations in Composite Materials

Liqun Cao, Keqi Li, Jianlan Luo and Yaushu Wong
Multiscale Modeling & Simulation 13 (4) 1446 (2015)
https://doi.org/10.1137/140999694

Regularity for Maxwell eigenproblems in photonic crystal fibre modelling

Monique Dauge, Richard A. Norton and Robert Scheichl
BIT Numerical Mathematics 55 (1) 59 (2015)
https://doi.org/10.1007/s10543-014-0487-z

Numerical Mathematics and Advanced Applications - ENUMATH 2013

Huoyuan Duan, Ping Lin and Roger C. E. Tan
Lecture Notes in Computational Science and Engineering, Numerical Mathematics and Advanced Applications - ENUMATH 2013 103 795 (2015)
https://doi.org/10.1007/978-3-319-10705-9_79

A recovery-based a posteriori error estimator for (curl) interface problems

Zhiqiang Cai and Shuhao Cao
Computer Methods in Applied Mechanics and Engineering 296 169 (2015)
https://doi.org/10.1016/j.cma.2015.08.002

A reduced model for the polarization in a ferroelectric thin wire

Antonio Gaudiello and Kamel Hamdache
Nonlinear Differential Equations and Applications NoDEA 22 (6) 1883 (2015)
https://doi.org/10.1007/s00030-015-0348-8

Optimal Sobolev Regularity for Linear Second-Order Divergence Elliptic Operators Occurring in Real-World Problems

Karoline Disser, Hans-Christoph Kaiser and Joachim Rehberg
SIAM Journal on Mathematical Analysis 47 (3) 1719 (2015)
https://doi.org/10.1137/140982969

Computation of Maxwell singular solution by nodal-continuous elements

Huo-Yuan Duan, Roger C.E. Tan, Suh-Yuh Yang and Cheng-Shu You
Journal of Computational Physics 268 63 (2014)
https://doi.org/10.1016/j.jcp.2014.02.044

Оптимальная эллиптическая регулярность в пространствах Соболева вблизи трехмерных многоматериальных вершин Неймана

Robert Haller-Dintelmann, Роберт Халер-Динтельман, Вольфганг Хeпнер, et al.
Функциональный анализ и его приложения 48 (3) 63 (2014)
https://doi.org/10.4213/faa3152

Edge Element Methods for Maxwell's Equations with Strong Convergence for Gauss' Laws

Patrick Ciarlet, Haijun Wu and Jun Zou
SIAM Journal on Numerical Analysis 52 (2) 779 (2014)
https://doi.org/10.1137/120899856

Optimal elliptic Sobolev regularity near three-dimensional multi-material Neumann vertices

R. Haller-Dintelmann, W. Höppner, H. -C. Kaiser, J. Rehberg and G. M. Ziegler
Functional Analysis and Its Applications 48 (3) 208 (2014)
https://doi.org/10.1007/s10688-014-0062-z

Quasi-optimal rates of convergence for the Generalized Finite Element Method in polygonal domains

Anna L. Mazzucato, Victor Nistor and Qingqin Qu
Journal of Computational and Applied Mathematics 263 466 (2014)
https://doi.org/10.1016/j.cam.2013.12.026

ON THE WELL-POSEDNESS, STABILITY AND ACCURACY OF AN ASYMPTOTIC MODEL FOR THIN PERIODIC INTERFACES IN ELECTROMAGNETIC SCATTERING PROBLEMS

BERANGERE DELOURME, HOUSSEM HADDAR and PATRICK JOLY
Mathematical Models and Methods in Applied Sciences 23 (13) 2433 (2013)
https://doi.org/10.1142/S021820251350036X

The polarization in a ferroelectric thin film: local and nonlocal limit problems

Antonio Gaudiello and Kamel Hamdache
ESAIM: Control, Optimisation and Calculus of Variations 19 (3) 657 (2013)
https://doi.org/10.1051/cocv/2012026

Optimal Control of Quasilinear $\boldsymbol{H}(\mathbf{curl})$-Elliptic Partial Differential Equations in Magnetostatic Field Problems

Irwin Yousept
SIAM Journal on Control and Optimization 51 (5) 3624 (2013)
https://doi.org/10.1137/120904299

Analysis of a continuous finite element method for $$H(\mathrm{curl},\mathrm{div})$$ -elliptic interface problem

Huoyuan Duan, Ping Lin and Roger C. E. Tan
Numerische Mathematik 123 (4) 671 (2013)
https://doi.org/10.1007/s00211-012-0500-x

Regularity of the Maxwell equations in heterogeneous media and Lipschitz domains

Andrea Bonito, Jean-Luc Guermond and Francky Luddens
Journal of Mathematical Analysis and Applications 408 (2) 498 (2013)
https://doi.org/10.1016/j.jmaa.2013.06.018

Further analysis of multilevel Monte Carlo methods for elliptic PDEs with random coefficients

A. L. Teckentrup, R. Scheichl, M. B. Giles and E. Ullmann
Numerische Mathematik 125 (3) 569 (2013)
https://doi.org/10.1007/s00211-013-0546-4

Error Estimates for a Vectorial Second-Order Elliptic Eigenproblem by the Local $L^2$ Projected $C^0$ Finite Element Method

Huo-Yuan Duan, Ping Lin and Roger C. E. Tan
SIAM Journal on Numerical Analysis 51 (3) 1678 (2013)
https://doi.org/10.1137/100812136

A Delta-Regularization Finite Element Method for a Double Curl Problem with Divergence-Free Constraint

Huoyuan Duan, Sha Li, Roger C. E. Tan and Weiying Zheng
SIAM Journal on Numerical Analysis 50 (6) 3208 (2012)
https://doi.org/10.1137/110850578

Convergence analysis of finite element methods for H(curl; Ω)-elliptic interface problems

Ralf Hiptmair, Jingzhi Li and Jun Zou
Numerische Mathematik 122 (3) 557 (2012)
https://doi.org/10.1007/s00211-012-0468-6

Multiple traces boundary integral formulation for Helmholtz transmission problems

R. Hiptmair and C. Jerez-Hanckes
Advances in Computational Mathematics 37 (1) 39 (2012)
https://doi.org/10.1007/s10444-011-9194-3

Finite Element Analysis of an Optimal Control Problem in the Coefficients of Time-Harmonic Eddy Current Equations

Irwin Yousept
Journal of Optimization Theory and Applications 154 (3) 879 (2012)
https://doi.org/10.1007/s10957-012-0040-7

Convergence of a discrete scheme in a regularization method for the quasi-steady Maxwell system in a nonhomogeneous conducting medium

M. V. Urev
Numerical Analysis and Applications 4 (3) 258 (2011)
https://doi.org/10.1134/S1995423911030086

Sobolev spaces on multiple cones

P. Auscher and N. Badr
Annales de la Faculté des sciences de Toulouse : Mathématiques 19 (3-4) 707 (2011)
https://doi.org/10.5802/afst.1264

Photonic Crystals: Mathematical Analysis and Numerical Approximation

Willy Dörfler, Armin Lechleiter, Michael Plum, Guido Schneider and Christian Wieners
Photonic Crystals: Mathematical Analysis and Numerical Approximation 1 (2011)
https://doi.org/10.1007/978-3-0348-0113-3_1

Direct computation of elliptic singularities across anisotropic, multi-material edges

R. Haller-Dintelmann, H.-Ch. Kaiser and J. Rehberg
Journal of Mathematical Sciences 172 (4) 589 (2011)
https://doi.org/10.1007/s10958-011-0207-z

Photonic Crystals: Mathematical Analysis and Numerical Approximation

Willy Dörfler, Armin Lechleiter, Michael Plum, Guido Schneider and Christian Wieners
Photonic Crystals: Mathematical Analysis and Numerical Approximation 23 (2011)
https://doi.org/10.1007/978-3-0348-0113-3_2

Unified Analysis of Leap-Frog Methods for Solving Time-Domain Maxwell’s Equations in Dispersive Media

Jichun Li
Journal of Scientific Computing 47 (1) 1 (2011)
https://doi.org/10.1007/s10915-010-9417-7

A combined nodal continuous–discontinuous finite element formulation for the Maxwell problem

Santiago Badia and Ramon Codina
Applied Mathematics and Computation 218 (8) 4276 (2011)
https://doi.org/10.1016/j.amc.2011.09.058

Compact Imbeddings in Electromagnetism with Interfaces between Classical Materials and Metamaterials

Lucas Chesnel and Patrick Ciarlet,
SIAM Journal on Mathematical Analysis 43 (5) 2150 (2011)
https://doi.org/10.1137/100810903

Multiscale Asymptotic Method for Maxwell's Equations in Composite Materials

Liqun Cao, Ya Zhang, Walter Allegretto and Yanping Lin
SIAM Journal on Numerical Analysis 47 (6) 4257 (2010)
https://doi.org/10.1137/080741276

Adaptive finite element methods for elliptic problems: Abstract framework and applications

Serge Nicaise and Sarah Cochez-Dhondt
ESAIM: Mathematical Modelling and Numerical Analysis 44 (3) 485 (2010)
https://doi.org/10.1051/m2an/2010010

Weighted regularization for composite materials in electromagnetism

Patrick Ciarlet Jr., François Lefèvre, Stéphanie Lohrengel and Serge Nicaise
ESAIM: Mathematical Modelling and Numerical Analysis 44 (1) 75 (2010)
https://doi.org/10.1051/m2an/2009041

Uniform estimates for transmission problems with high contrast in heat conduction and electromagnetism

Gabriel Caloz, Monique Dauge and Victor Péron
Journal of Mathematical Analysis and Applications 370 (2) 555 (2010)
https://doi.org/10.1016/j.jmaa.2010.04.060

Multiscale Computations for 3D Time-Dependent Maxwell's Equations in Composite Materials

Ya Zhang, Li-Qun Cao and Yau-Shu Wong
SIAM Journal on Scientific Computing 32 (5) 2560 (2010)
https://doi.org/10.1137/080740337

A posteriori error estimator based on gradient recovery by averaging for discontinuous Galerkin methods

Emmanuel Creusé and Serge Nicaise
Journal of Computational and Applied Mathematics 234 (10) 2903 (2010)
https://doi.org/10.1016/j.cam.2010.03.027

Computation of the band structure of two-dimensional photonic crystals with hp finite elements

K. Schmidt and P. Kauf
Computer Methods in Applied Mechanics and Engineering 198 (13-14) 1249 (2009)
https://doi.org/10.1016/j.cma.2008.06.009

The adaptive immersed interface finite element method for elliptic and Maxwell interface problems

Zhiming Chen, Yuanming Xiao and Linbo Zhang
Journal of Computational Physics 228 (14) 5000 (2009)
https://doi.org/10.1016/j.jcp.2009.03.044

Finite element approximation of Maxwell eigenproblems on curved Lipschitz polyhedral domains

Anahí Dello Russo and Ana Alonso
Applied Numerical Mathematics 59 (8) 1796 (2009)
https://doi.org/10.1016/j.apnum.2009.01.007

A FEM-BEM approach for electro-magnetostatics and time-harmonic eddy-current problems

Ana Alonso Rodríguez and Alberto Valli
Applied Numerical Mathematics 59 (9) 2036 (2009)
https://doi.org/10.1016/j.apnum.2008.12.002

The Local $L^2$ Projected $C^0$ Finite Element Method for Maxwell Problem

Huo-Yuan Duan, Feng Jia, Ping Lin and Roger C. E. Tan
SIAM Journal on Numerical Analysis 47 (2) 1274 (2009)
https://doi.org/10.1137/070707749

The Mortar-Discontinuous Galerkin Method for the 2D Maxwell Eigenproblem

Annalisa Buffa, Ilaria Perugia and Tim Warburton
Journal of Scientific Computing 40 (1-3) 86 (2009)
https://doi.org/10.1007/s10915-008-9238-0

Equilibrated error estimators for discontinuous Galerkin methods

Sarah Cochez‐Dhondt and Serge Nicaise
Numerical Methods for Partial Differential Equations 24 (5) 1236 (2008)
https://doi.org/10.1002/num.20315

Boundary observability of a numerical approximation scheme of Maxwell’s system in a cube

Serge Nicaise
Collectanea mathematica 59 (1) 27 (2008)
https://doi.org/10.1007/BF03191180

Lorenz‐gauged vector potential formulations for the time‐harmonic eddy‐current problem with L∞‐regularity of material properties

Paolo Fernandes and Alberto valli
Mathematical Methods in the Applied Sciences 31 (1) 71 (2008)
https://doi.org/10.1002/mma.900

Adaptive finite element techniques for the Maxwell equations using implicit a posteriori error estimates

D. Harutyunyan, F. Izsák, J.J.W. van der Vegt and M.A. Botchev
Computer Methods in Applied Mechanics and Engineering 197 (17-18) 1620 (2008)
https://doi.org/10.1016/j.cma.2007.12.006

A Locally Divergence-Free Interior Penalty Method for Two-Dimensional Curl-Curl Problems

Susanne C. Brenner, Fengyan Li and Li-Yeng Sung
SIAM Journal on Numerical Analysis 46 (3) 1190 (2008)
https://doi.org/10.1137/060671760

W1,q REGULARITY RESULTS FOR ELLIPTIC TRANSMISSION PROBLEMS ON HETEROGENEOUS POLYHEDRA

J. ELSCHNER, H.-C. KAISER, J. REHBERG and G. SCHMIDT
Mathematical Models and Methods in Applied Sciences 17 (04) 593 (2007)
https://doi.org/10.1142/S0218202507002030

A discontinuous Galerkin method on refined meshes for the two-dimensional time-harmonic Maxwell equations in composite materials

Stephanie Lohrengel and Serge Nicaise
Journal of Computational and Applied Mathematics 206 (1) 27 (2007)
https://doi.org/10.1016/j.cam.2006.05.020

FOSLL? Method for the Eddy Current Problem with Three-Dimensional Edge Singularities

Eunjung Lee and Thomas A. Manteuffel
SIAM Journal on Numerical Analysis 45 (2) 787 (2007)
https://doi.org/10.1137/050647001

Discontinuous Galerkin computation of the Maxwell eigenvalues on simplicial meshes

Annalisa Buffa, Paul Houston and Ilaria Perugia
Journal of Computational and Applied Mathematics 204 (2) 317 (2007)
https://doi.org/10.1016/j.cam.2006.01.042

Mortar finite element discretization for the flow in a nonhomogeneous porous medium

Christine Bernardi, Frédéric Hecht and Zoubida Mghazli
Computer Methods in Applied Mechanics and Engineering 196 (8) 1554 (2007)
https://doi.org/10.1016/j.cma.2006.03.018

Multifield Problems in Solid and Fluid Mechanics

Dorothee Knees and Anna-Margarete Sändig
Lecture Notes in Applied and Computational Mechanics, Multifield Problems in Solid and Fluid Mechanics 28 331 (2006)
https://doi.org/10.1007/978-3-540-34961-7_10

Discontinuous Galerkin Approximation of the Maxwell Eigenproblem

Annalisa Buffa and Ilaria Perugia
SIAM Journal on Numerical Analysis 44 (5) 2198 (2006)
https://doi.org/10.1137/050636887

Discrete Compactness for the hp Version of Rectangular Edge Finite Elements

Daniele Boffi, Martin Costabel, Monique Dauge and Leszek Demkowicz
SIAM Journal on Numerical Analysis 44 (3) 979 (2006)
https://doi.org/10.1137/04061550X

Interpolation estimates for edge finite elements and application to band gap computation

Daniele Boffi and Lucia Gastaldi
Applied Numerical Mathematics 56 (10-11) 1283 (2006)
https://doi.org/10.1016/j.apnum.2006.03.014

Existence, Uniqueness, and Regularity Results for Piezoelectric Systems

D. Mercier and S. Nicaise
SIAM Journal on Mathematical Analysis 37 (2) 651 (2005)
https://doi.org/10.1137/040617728

EXPONENTIAL CONVERGENCE OF hp-FEM FOR MAXWELL EQUATIONS WITH WEIGHTED REGULARIZATION IN POLYGONAL DOMAINS

MARTIN COSTABEL, MONIQUE DAUGE and CHRISTOPH SCHWAB
Mathematical Models and Methods in Applied Sciences 15 (04) 575 (2005)
https://doi.org/10.1142/S0218202505000480

Operator Theoretical Methods and Applications to Mathematical Physics

Martin Costabel, Monique Dauge and Serge Nicaise
Operator Theoretical Methods and Applications to Mathematical Physics 241 (2004)
https://doi.org/10.1007/978-3-0348-7926-2_28

Topics in Computational Wave Propagation

Martin Costabel and Monique Dauge
Lecture Notes in Computational Science and Engineering, Topics in Computational Wave Propagation 31 125 (2003)
https://doi.org/10.1007/978-3-642-55483-4_4

Multigrid methods for the computation of singular solutions and stress intensity factors III: interface singularities

Susanne C. Brenner and Li-yeng Sung
Computer Methods in Applied Mechanics and Engineering 192 (41-42) 4687 (2003)
https://doi.org/10.1016/S0045-7825(03)00455-9

Singularities of eddy current problems

Martin Costabel, Monique Dauge and Serge Nicaise
ESAIM: Mathematical Modelling and Numerical Analysis 37 (5) 807 (2003)
https://doi.org/10.1051/m2an:2003056

Minimal regularity of the solutions of some transmission problems

D. Mercier
Mathematical Methods in the Applied Sciences 26 (4) 321 (2003)
https://doi.org/10.1002/mma.356

Theoretical tools to solve the axisymmetric Maxwell equations

F. Assous, P. Ciarlet and S. Labrunie
Mathematical Methods in the Applied Sciences 25 (1) 49 (2002)
https://doi.org/10.1002/mma.279

A Posteriori Error Estimators for Elliptic Equations with Discontinuous Coefficients

Martin Petzoldt
Advances in Computational Mathematics 16 (1) 47 (2002)
https://doi.org/10.1023/A:1014221125034

The ℎ𝑝-local discontinuous Galerkin method for low-frequency time-harmonic Maxwell equations

Ilaria Perugia and Dominik Schötzau
Mathematics of Computation 72 (243) 1179 (2002)
https://doi.org/10.1090/S0025-5718-02-01471-0

Construction of Nearly Orthogonal Nedelec Bases for Rapid Convergence with Multilevel Preconditioned Solvers

Din-Kow Sun, Jin-Fa Lee and Zoltan Cendes
SIAM Journal on Scientific Computing 23 (4) 1053 (2001)
https://doi.org/10.1137/S1064827500367531

EXISTENCE, UNIQUENESS AND REGULARITY FOR SOLUTIONSV OF THE CONICAL DIFFRACTION PROBLEM

JOHANNES ELSCHNER, RAINER HINDER, GUNTHER SCHMIDT and FRANK PENZEL
Mathematical Models and Methods in Applied Sciences 10 (03) 317 (2000)
https://doi.org/10.1142/S0218202500000197

Exact Boundary Controllability of Maxwell's Equations in Heterogeneous Media and an Application to an Inverse Source Problem

Serge Nicaise
SIAM Journal on Control and Optimization 38 (4) 1145 (2000)
https://doi.org/10.1137/S0363012998344373